It is more a non-feminist woman trying to persuade feminist women to give up on something for the sake of men. XD

Men do have a choice to be stay-at-home dads. But it usually has a higher cost since they usually make more money.

As for your claim that "Men never had rights to their children" is simply not true. Historically, children carry their names (not the mother's name). And they were the ones who decided over them. Like who to marry. It is just recently (not even a century) that custody can be granted to women. And even now, when men ask for custody, they have a high chance that it is granted 50/50.

https://www.huffpost.com/entry/dispelling-the-myth-of-ge_b_1617115

Maybe what is needed is just time. As men become more involved in child rising, more custodies would be granted.